L = { am b2^n | m,n > 0 }
Present a CSG for L to show it is context sensitive
Context Sensitive Grammar
S → AXaY
Xa → aaX
XY → ZY
XY → M
aZ → Za
AZ → AX
aM → Ma
AM → ϵ
There exists a context sensitive grammar for the given language. So, it is context sensitive language.
Suppose X1, .. ,XM are independent, identically distributed random variables with mean a and variance b2. Let aM ≡ (1/M)Σi=1M aM and bM2≡ (1/(M-1)) Σi=1M (Xi-aM)2. a) Show that aM is an unbiased estimator of E[X]: that is, E[aM] = a. b) Assume that the identity E[ Σi=1M (Xi-aM)2 ] = (M-1) b2 is correct. Show that bM2 is an unbiased estimator of var(X): that is, E[bM2] = b2
construct a context free grammar for the language l {a^nc^mb^n: n,m Greaterthanorequalto 0}
Show that L= {a^nb^n | n>= 0, n is not a multiple of 5} is context free.
(a) Show that L = { a^n b^2m a^n : n, m >= 0 } is a CFL by drawing a nondeterministic PDA M that accepts L. Show a formal computation (i.e., sequence of instantaneous descriptions) of your machine M for each of the following five strings w: aa, ab^2a, a^2 b^4 a^2, abbab. (b) For each of the above five strings w, state whether or not w L(M) and explain why
Let L be the language {0n 1m : n ≤ m ≤ 2n}. Is L regular? contextfree but not regular? or not context-free? Show that your answer is correct.
Problem 8 You can assume that L = {a"be": n > 0} is not context free. Prove the following: Show that L-ab: n20 is not context free Show that L = {w E {a,b,c,d)* : na(w) = nb(w)-ne(w) = nd(w)) is not context free Note that na(w) means the number of a's in w .
Exercise 7.3.2: Consider the following two languages: Li = {a"b2ncm n,m >0} L2 = {a" mc2m | n,m >0} a) Show that each of these languages is context-free by giving grammars for each. ! b) Is L; n L, a CFL? Justify your answer.
PDA for L = {0^n 0^m | n and m > 0} and do computation or input string 00001111
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0 < n < m} is not context-free. 2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0
Exercise 25: Let f: [0,1R be defined by x=0 fx)/n, m/n, with m, n E N and n is the minimal n such that z m/n x- m/n, with m,n E N and n is the minimal n such that x a) Show that L(f, P) = 0 for all partitions P of [0, 1]. b) Let m E N. Show that the cardinality of the set A :-{х є [0, 1] : f(x) > 1/m} is bounded by m(m...